To summarize, both jquery and dojo are good. To simply say JQuery is like .net and dojo is like java. So JQuery is simple to use, less code, better speed and seemlessly integrates with asp.net web / mvc pages where as dojo needs some learning / tweaking / experimenting to achieve easy scalable web pages using built-in solutions. Dojo is ideal for large scale / high traffic web sites.

It may be good idea to start using/experimenting dojo with any new web page or mobile app as jquery mobile is still in beta (though lot of apps built using jquery).